Cables, pulleys, 2 weights

  • #1
DylanMurfly
3
0
Homework Statement
I've been struggling with this question for a while now, and for the life of me i cant see what i'm missing, the picture is in the solution attempt along with the equations i've been using. Any assistance would be amazing. Find: Tension AB and Angle a
Relevant Equations
W1 = 330g
W2 = 440g
1713386600869.png

Fx = 0 = ABcos(a)+BCcos(b)-BDcos(30)
Fy = 0 = ABsin(a)+BCsin(b)-BDsin(30)

==

Fx = 0 = ABcos(a) + 3.2737cos(b) - 3.738
Fy = 0 = ABsin(a) + 3.237sin(b) - 2.158

But i cant find a third equation to use. I've tried a+b = 90 but that produced a number of errors. Thank you.
Edit: angle b is the angle string CB makes with horizontal
 
Last edited:
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  • #2
Please post the question that the problem asks. What are you looking for? The homework statement must be as was given to you.
 
  • #3
kuruman said:
Please post the question that the problem asks. What are you looking for? The homework statement must be as was given to you.
updated, sorry about that
 
  • #4
Finding the tension AB is easy. You are missing that when the sum of N vectors is zero and you draw the vector addition diagram, the ensuing shape is a closed polygon with N sides. Apply this idea here.
 
  • #5
Thank you sir, got it all fixed up now, didn't even think to go about it that way, earlier response was a brain fart as its quite early in the morning and i haven't had a coffee yet.
 

FAQ: Cables, pulleys, 2 weights

1. How do pulleys affect the tension in cables?

Pulleys change the direction of the tension force in a cable. When a weight is suspended from a pulley, the tension in the cable is equal to the weight being lifted, assuming the pulley is frictionless and massless. If multiple pulleys are used, the tension can be distributed across the system, allowing for a mechanical advantage that makes lifting easier.

2. What is the mechanical advantage of using a pulley system with two weights?

The mechanical advantage of a pulley system depends on the configuration of the pulleys and the number of segments of cable supporting the weights. For example, in a simple fixed pulley, the mechanical advantage is 1, meaning you exert the same force as the weight. In a block and tackle system, the mechanical advantage can be greater than 1, allowing you to lift heavier loads with less effort.

3. How do you calculate the forces acting on two weights connected by a cable and pulley?

To calculate the forces, you need to apply Newton's second law (F = ma) to each weight. If the system is in equilibrium, the sum of the forces acting on each weight must equal zero. You can set up equations based on the weights, the tension in the cable, and any acceleration if the system is moving. Solving these equations simultaneously will give you the tension and the forces acting on each weight.

4. What factors can affect the efficiency of a pulley system with cables and weights?

The efficiency of a pulley system can be affected by several factors, including friction in the pulleys, the mass of the pulleys themselves, the stiffness of the cables, and any additional forces acting on the system, such as air resistance. Reducing friction and using lightweight materials can help improve efficiency, making it easier to lift weights with less input force.

5. Can a pulley system be used to lift objects vertically and horizontally?

Yes, a pulley system can be designed to lift objects both vertically and horizontally. Vertical lifting is the most common application, where pulleys are used to raise weights straight up. For horizontal movement, a system of pulleys can redirect the force, allowing objects to be pulled along a surface. The configuration of the pulleys will determine the effectiveness and efficiency of the system in each direction.

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